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Answer :
Final answer:
To find the percentage of GMAT scores between 347 and 647, find the z-scores and use a z-table to calculate the cumulative area.
Explanation:
To find the percentage of GMAT scores between 347 and 647, we need to find the area under the bell curve between these two scores. First, we need to find the z-scores for both scores using the formula z = (x - μ) / σ. For 347, the z-score is (-200) / 100 = -2, and for 647, the z-score is 100 / 100 = 1.
Next, we need to find the percentage of data between these z-scores. We can use a z-table to find the cumulative area. The cumulative area for -2 is 0.0228 and for 1 is 0.8413.
To find the percentage between these two z-scores, we subtract the cumulative area for -2 from the cumulative area for 1: 0.8413 - 0.0228 = 0.8185.
Therefore, the percentage of GMAT scores between 347 and 647 is 81.85%.
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Answer:
16%; 2.5%; 34%; 81.5%
Step-by-step explanation:
Using the empirical rule, we know that 68% of data falls within one standard deviation of the mean; 95% of data falls within two standard deviations of the mean; and 99.7% of data falls within 3 standard deviations of the mean.
This means from the mean to 1 standard deviation (σ) above is 34% of data; from the mean to 1 σ below is 34% of data; from 1 σ to 2σ above is 13.5% of data; from 1σ to 2σ below is 13.5% of data; from 2σ to 3σ above is 2.35% of data; from 2σ to 3σ below is 2.35% of data; more than 3σ above is 0.15% of data; and more than 3σ below is 0.15% of data.
647 is 1 σ above the mean. This means that we go from here above;
13.5+2.35+0.15 = 16%
747 is 2σ above the mean. This means that we go from here above:
2.35+0.15 = 2.5%
447 is 1σ below the mean and 547 is the mean. This means that we have 34%.
347 is 2σ below the mean and 647 is 1 above the mean. This means we go from:
13.5+34+34 = 81.5%
